In this paper, we discuss the criteria that should be satisfied by a descriptor for nonrigid shapes with a single closed contour. We then propose a shape representation method that fulfills these criteria. In the proposed approach, contour convexities and concavities at different scale levels are represented using a two-dimensional (2-D) matrix. The representation can be visualized as a 2-D surface, where "hills" and "valleys" represent contour convexities and concavities, respectively. The optimal matching of two shape representations is achieved using dynamic programming and a dissimilarity measure is defined based on this matching. The proposed algorithm is very efficient and invariant to several kinds of transformations including some articulations and modest occlusions. The retrieval performance of the approach is illustrated using the MPEG-7 shape database, which is one of the most complete shape databases currently available. Our experiments indicate that the proposed representation is well suited for object indexing and retrieval in large databases. Furthermore, the representation can be used as a starting point to obtain more compact descriptors.